April 2016
Intermediate to advanced
478 pages
14h 44m
English
Content preview from Combinatorics of Permutations, 2nd Edition
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3
In Many Circ les. Permutations as Products
of Cycles.
3.1 Decomposing a Permutation into Cycles
So far we have looked at permutations as linear orders, that is, ways of listing
n objects so that each object gets listed exactly once. In this section we will
discuss permutations from a different viewpoint. We will consider them as
functions. Let us redefine permutations along these lines.
DEFINITION 3.1 Let f :[n] → [n] be a bijection. Then we say that f
is a permutation of the set [n].
This definition certainly does not contradict our former definition of permu-
tations. Formerly, we said that 34152 was a permutation of length five. Now
we can reformulate
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